When you try to stop your car in an emergency, there is some time before you can react.Your car is going 25 m/s and your reaction time is 0.20 s, then after you hit your brakes it decelerates at 9.5 m/s2. How far will your car travel before it stops?
geez, again?
It takes t = 25/9.5 seconds to stop once the brakes are applied.
s = 25*0.2 + 25t - 4.75 t^2 is the total stopping distance
I think I remember that as well.
To calculate the distance the car will travel before it stops, we need to consider two factors: the distance covered during the reaction time and the distance covered while decelerating.
1. Calculate the distance covered during the reaction time:
During the reaction time, the car will continue to travel at its initial velocity of 25 m/s for a duration of 0.20 s. The formula to calculate the distance covered during uniform motion is:
Distance = Velocity × Time
Therefore, the distance covered during the reaction time is:
Distance = 25 m/s × 0.20 s
Distance = 5 meters
2. Calculate the distance covered while decelerating:
After the reaction time, the car starts to decelerate at a rate of 9.5 m/s^2 until it comes to a stop. To calculate the distance covered while decelerating, we can use the following formula from kinematics:
Distance = (Velocity^2 - Initial Velocity^2) / (2 × Acceleration)
The final velocity will be 0 m/s since the car comes to a stop. Plugging in the values:
Distance = (0^2 - 25^2) / (2 × -9.5 m/s^2)
Distance = (-625) / (-19 m/s^2)
Distance ≈ 32.9 meters
3. Calculate the total distance:
The total distance covered will be the sum of the distance covered during the reaction time and the distance covered while decelerating:
Total Distance = Distance during reaction time + Distance while decelerating
Total Distance = 5 meters + 32.9 meters
Total Distance ≈ 37.9 meters
Therefore, your car will travel approximately 37.9 meters before it stops.